## moongazer 3 years ago If tan (theta) =5/4 and cos (theta) < 0 . Find the other trig. functions. Could someone check my answers?

1. moongazer

am I right that theta is in quadrant 3 ?

2. Silent_Sorrow

Yup, so Sin (theta) < 0 as well

3. moongazer

4. waterineyes

5. moongazer

ok

6. moongazer

$\sin \theta =(-5\sqrt{41})/41$ $\cos \theta = (-4\sqrt{41})/41$ $\tan \theta = 5/4$ $\csc \theta = -\sqrt{41}/5$ $\sec \theta =-\sqrt{41}/4$ $\cot \theta = 4/5$

7. moongazer

Am I correct?

8. Silent_Sorrow

|dw:1341743660142:dw| Just remember "All Science Teachers Crazy" so in the first quad all trig functions are positive, in the 2nd all Sine functions are positive, in the 3rd all Tangent functions are positive so in the 4th all Cosine functions are positive.

9. moongazer

10. moongazer

Could someone check it?

11. moongazer

12. mathslover

when cos theta is negative then theta lies in 2nd quadrant ..

13. moongazer

@mathslover why?

14. mathslover

15. moongazer

ok thanks :)

16. mathslover

Remember this :Quadrant 1: Cosine is positive and Sine is positive. (x > 0 ; y > 0) just as ( cos(theta) > 0 ; sin(theta) > 0) Quadrant 2: Cosine is negative and Sine is positive. (x < 0; y > 0) just as ( cos(theta) < 0 ; sin(theta) > 0) Quadrant 3: Cosine is negative and Sine is negative. (x < 0 ; y < 0) just as ( cos(theta) < 0 ; sin(theta)< 0) Quadrant 4: Cosine is positive and Sine is negative. ( x > 0 ; y < 0 ) just as ( cos(theta) > 0 ; sin(theta) < 0)

17. mathslover

@moongazer

18. moongazer

I am here

19. mathslover

So did u get that quadrant 2 : cos theta is negative ?

20. moongazer

21. mathslover

Take ur time

22. moongazer

But in quadrant 3 cos theta is also negative so why I can't choose it as the location of theta?

23. moongazer

isn't it that tan theta is positive in quadrant 3 and according to the given tan theta is positive. So choosing that theta is in quadrant 3 is better?

24. mathslover

oh yes u r also right but i am not perfect in this topic may be @lalaly do it for u

25. moongazer

@lalaly My answers are correct right?

26. lalaly

u can describe this as a right triangle $\tan (\theta)=\frac{opposite}{adjacent}=\frac{5}{4}$so from this u know that opposite=5 and adjacent =4 |dw:1341746704835:dw|

27. lalaly

now use those values to find the ratios for the other trig functions

28. moongazer

But isn't it I can also view as|dw:1341747710304:dw|

29. moongazer

Are my answers right or wrong?

30. ash2326

@moongazer you are correct :D

31. moongazer

@ash2326 Thanks for that!

32. ash2326

you wanna see, the pic I made to check this?

33. moongazer

ok, let me see it :)

34. ash2326

here it is

35. moongazer

That is also what I am thinking :)

36. ash2326

Yay:D